Documentation

Lean.Meta.Tactic.Grind.Propagate

Propagates equalities for a conjunction a ∧ b based on the truth values of its components a and b. This function checks the truth value of a and b, and propagates the following equalities:

  • If a = True, propagates (a ∧ b) = b.
  • If b = True, propagates (a ∧ b) = a.
  • If a = False, propagates (a ∧ b) = False.
  • If b = False, propagates (a ∧ b) = False.
Equations
    Instances For

      Propagates truth values downwards for a conjunction a ∧ b when the expression itself is known to be True.

      Equations
        Instances For

          Propagates equalities for a disjunction a ∨ b based on the truth values of its components a and b. This function checks the truth value of a and b, and propagates the following equalities:

          • If a = False, propagates (a ∨ b) = b.
          • If b = False, propagates (a ∨ b) = a.
          • If a = True, propagates (a ∨ b) = True.
          • If b = True, propagates (a ∨ b) = True.
          Equations
            Instances For

              Propagates truth values downwards for a disjuction a ∨ b when the expression itself is known to be False.

              Equations
                Instances For

                  Propagates equalities for a negation Not a based on the truth value of a. This function checks the truth value of a and propagates the following equalities:

                  Equations
                    Instances For

                      Propagates truth values downwards for a negation expression Not a based on the truth value of Not a. This function performs the following:

                      Equations
                        Instances For
                          Equations
                            Instances For

                              Propagates Eq upwards

                              Equations
                                Instances For

                                  Propagates Eq downwards

                                  Equations
                                    Instances For

                                      Propagates EqMatch downwards

                                      Equations
                                        Instances For

                                          Propagates HEq downwards

                                          Equations
                                            Instances For

                                              Propagates HEq upwards

                                              Equations
                                                Instances For

                                                  Propagates ite upwards

                                                  Equations
                                                    Instances For

                                                      Propagates dite upwards

                                                      Equations
                                                        Instances For